Ernst Julius Berg.

Electrical energy, its generation, transmission, and utilization online

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SB 33 307








Lectures Given at Union University



Published by the

McGraw-Hill Book. Company


\Succe.s.sons to the Book Departments of the

McGraw Publishing Company Hill Publishing Company

Publishers of Books for

Electrical World The Enonneering" and Mining Journal

The Engineering Record R>wer and The Engineer

Electric Railway Journal American Machinist


THIS book is compiled from a series of lectures intended to
bridge the theoretical instructions given in the ordinary univer-
sity education, and the practical problems confronted in com-
mercial engineering. The sequence of the various phenomena
discussed is not, therefore, so logical as would be the case if a
book on electrical phenomena had been attempted. Jt is hoped,
however, that the arrangement will prove of practical help.

Since many of the questions pertaining to practical engineer-
ing cannot be answered by a strictly theoretical calculation,
without going into too complex mathematics, some approximate
equations have been given, sufficiently accurate for most prac-
tical purposes.

Obviously, there can be little originality in the fundamental
equations. Almost all problems, however intricate, have been
solved ; and the difficulty, if not impossibility, of giving due
credit has determined the author to omit all references.

I wish to express my warm appreciation and thanks to Dr.
Charles P. Steinmetz and Dr. Edwin Wilbur Rice, Jr., whose
advice during several years of practical work in Electrical
Engineering have materially assisted me ; to Mr. Otto Holz,
who not only has taken an active part in preparing the book,
but has also helped in the proof-reading ; to Mr. O. A. Kenyon,
who has followed the book through publication, and arranged
the notations in conformity with the International Standard : and,
finally, to the McGraw Publishing Company, for its generous
cooperation in bringing out the work.

E. J. B.



Relative merits of direct-current and various alternating-current

systems 4

Effects of voltage on spacing of transmission wires 3

Determination of most economical voltage in power transmissions .5


Equations for determining the resistance, inductance and capacity

with commercial arrangements of wires 7-15

Numerical instances 15

Average inductance and capacity in high-potential lines. Frequency.

Standard frequencies. Determination of the natural frequency.

Bearing of the natural frequency of the line on the choice of

frequency 16-20

Discussion of most likely higher harmonic in a transmission line . . 18

Capacity reactance and inductive reactance 19

Graphic representation of line phenomena 22

Algebraic method of determination of line characteristics 24

Principles of algebra of complex quantities . 26

Complex quantities applied to line calculations 27

Maximum output of a transmission line 32

Expression of power and apparent power in complex quantities ... 33

Effects of open circuits and short circuits in transmission lines ... 34

Transformer connections in high-potential lines 37

Advisability of grounding of neutral in transmission lines 38

Investigation of corona effects in air, and in insulated wires .... 38

Minimum distances to avoid corona 40

Effects of accidental grounds 42

General equation of phenomena due to accidental grounds 43

Static stresses in transformers due to accidental grounds 46

How to ground the neutral 47

Apparent erratic voltage to ground 48

Tabulation of numerical constants in transmission lines , 49

Rating of cables, maximum voltage 50

Skin effects in solid and stranded copper and aluminium conductors . 52

Inductance and capacity in concentric cables 53

Effect of lead covering in cables 54




Effect of iron armour on constants of cables 59

Numerical instances of cable calculations . 60

Iron conductors and cables used as electrical conductors 62

Telephone line. Inductive and static effects with various commer-
cial arrangements of wires 63

Striking distances 73

Wire table 73

Cost of various types of transmission constructions 74


Prime Movers. Steam turbines, general characteristics of different

types, steam velocities used 75

The meaning of efficiency 76

Determination of available energy in superheated and saturated

steam 77

Thermal efficiency 78

Saving coal and water by superheat 78, 82

Reciprocating engines, when best suited 83

Combination of reciprocating engines and steam turbines 83

Gas engines 83

Relation between generator voltage and voltage transmission lines . 84

Switchboard arrangements 86


Necessary tests to determine characteristics 87

No-load saturation test 87

Armature reaction in machines of definite poles and distributed field

winding 88

Armature self-induction or reactance depending upon the type of

generator 90

Synchronous impedance test 90

Numerical instances 91

Graphical method of determining the induced E.M.F. and the field

excitation 93-95

Algebraic methods of determining the field excitation for various loads 95

Determination of mechanical displacement of armature with load . . 98

Stability as depending upon constants and type of generator .... 103

Synchronizing force 103

Hunting of alternators. Theory and numerical instances for different

types 105

Parallel operation of alternators 112

Cross currents caused by pulsation in speed and excitation 113

Energy transfer by the fundamental and triple frequency current . . 116

Mechanical arrangements necessary in rigidly connected alternators . 116

E. W. Rice compensated alternator, theory and numerical instance . 117



Alexanderson self-exciting alternator 120

Induction alternator, its limitations and rating in connection with

synchronous generators 123

Half-frequency generator 125

Inductor alternator . ., 128

Double-current generator 129

Synchronizing of alternators 129

Instantaneous very large currents in synchronizing 131

Wave shape of alternators 132

Instances from tests 132-136

Interesting data on modern generators of different types 135

Transformers. Core type and shell type, single phase and three-phase
transformers. Connections of single-phase transformers for multi-
phase work. Two-phase, three-phase transformation, single-phase

and multiphase compensators 137

Transformers in series and multiple connection 147-149

Losses, efficiency and regulation of transformers 150

Abnormal currents taken by transformers 160

Instruments. Direct-current voltmeters and ammeters 161

Alternating-current volt and ammeters, electrostatic voltmeter . . 163

Sparkgap as voltmeter. Compensation for line drop 164-165

Wattmeters and watthour meters of commutator and inductance

type. Curve drawing and recording instruments 166

Multiphase meters, limitations of various types 166

Power-factor indicator. Synchronism indicators, frequency indi-
cators 172, 176

Oscillograph 176

Protection of apparatus in generating station 178



1. Inductance between parallel conductors 9

2. Capacity between parallel conductors 11

3. Wave shape of Delta-connected alternator 18

4. Wave shape of Y-connected alternator 18

5. Graphic solution of e non-inductive current 22

6. Graphic solution of e 30 lagging current 23

7. Graphic solution of e 30 leading current 23

8. Algebraic method ...'.. '<*?, 24

9. Complex expression of current 26

10. Complex expression of current 26

11. Complex expression of current impedance 26

12. Constants at receiving end of line 32

13. Corona effects in parallel conductors 39

14. Effect of leaks in switches . 42

15. Effect of grounds in systems 42

16. Balanced three-phase system 43

17. Effect of ground 43

18. Effect of ground balanced system 45

19. Effect of ground unbalanced system 45

20. Electrostatic stresses in generator 46

21. Capacity effects in generators and transformers 46

22. Balanced capacity in systems . . 46

23. Static stresses with one high-potential line grounded 47

24. Erratic ground . . . . 48

25. Skin effect, resistance coefficient 52

26. Inductance of concentric conductors .....'.... i ... 53

27. Grounded lead-covered cable 54

28. Grounded lead-covered cable ".' 54

29. Grounded lead-covered cable 54

30. Grounded lead-covered cable 55

31. Single conductor lead -covered cable 56

32. Lead-covered, not grounded cable 58

33. Telephone line disturbances 65

34. Telephone line disturbances 66

35. Telephone line disturbances 67

36. Telephone line disturbances 69




37. Theoretical water rates 79

38. Theoretical water rates 79

39. Theoretical water rates . ; 80

40. Theoretical water rates 80

41. Theoretical water rates . . . 81

42. Theoretical water rates 81

43. Theoretical water rates 83

44. Effect of superheat . 84

45. Switchboard -. ., 86

46. Saturation curve of alternator 87

47. Armature reaction of alternator 88

48. Armature reaction of alternator 88

49. Synchronous impedance curve 89

50. Synchronous impedance curve 90

51. Vector diagram of alternator 93

52. Vector diagram of alternator 93

53. Vector diagram of alternator 94

54. Vector diagram of alternators 94

55. Vector diagram of alternators 95

56. Saturation curve of alternator 96

57. Phase characteristic 98

58. Compounding curve of alternator 101

59. Phase characteristic 101

60. Hunting of alternators 106

61. Natural frequency 110

62. Natural period ........ 112

63. Pulsation in engine speed 113

64. E.M.F. corresponding to engine pulsation 113

65. Compensated alternator 117

66. Alexander alternator 121

67. Self-excited alternator . . . 122

68. Inductor alternator .' 128

69. Synchronizing of alternators 130

70. Synchronizing of alternators 130

71. Synchronizing of alternators 130

72. Synchronizing of alternators . .' 131

73. No-load E.M.F. of alternator 132

74. Terminal E.M.F. of alternator 133.

75. Full-load E.M.F. of alternator . . V 134

76. Terminal voltage of alternator 134

77. Current in neutral of alternator 135

78. Potential in ground connection of alternator 130

79. Single-phase core type transformer 137

80. Single-phase shell type transformer 137

81. Three-phase core type transformer 137

82. Three-phase shell type transformer * 137



83. Resultant E.M.F. core-type transformer . 138

84. Resultant E.M.F. shell-type transformer . . 138

85. Resultant E.M.F. shell-type transformer 139

86. Transformer connection 140

87. Transformer connection 140

88. Transformer connection 140

89. Transformer connection 140

90. Transformer connection 141

91. Transformer connection 141

92. Two-phase, three-phase transformer 141

93. Single-phase compensator 143

94. Two-phase, three-phase compensator 144

95. Three-phase, two-phase compensator 146

96. Series-connected transformers 148

97. Parallel connected transformers 149

98. Exciting current, single-phase transformer 150

99. E.M.F. of generator 151

100. Exciting current of transformer 152

101. Line current 152

102. Neutral current and exciting current . 152

103. Transformer voltage and current 153

104. Triple harmonic exciting current 154

105. Transformer voltage 154

106. Transformer voltage , . 155

107. Regulation of transformers 158

108. Hysteresis cycle of sheet iron 160

109. Connections for volt and ammeters 163

110. Connections for volt and ammeters 164

111. Instruments for line-drop compensation 165

112. Wattmeter connections 166

113. Wattmeter connections 166

114. Single-phase wattmeter in three-phase circuit 166

115. Single-phase wattmeter in three-phase circuit 166

116. Single-phase wattmeter in three-phase circuit 166

117. Two single-phase meters in multiphase system 170

118. Single-phase meter in balance multiphase system 171

119. Diagram of phase relation 172

120. Power-factor indicator . 173








IN the following treatise it has been assumed that the student
is in a general way familiar with the fundamental principles of
electrical engineering and to some extent with the theories of
the various phenomena and apparatus involved. For this
reason, when the equations used are found in elementary text-
books, no endeavor is made to deduce ,them, but their applica-
tion to practical problems is given. The deductions arc, how-
ever, made when not otherwise readily available.

The subject will be treated from the consulting and designing
engineers' point of view, therefore such practical and theoreti-
cal questions will be discussed, as are met by engineers of
electrical manufacturing companies. Whenever possible, a
general discussion will be given covering the widest range of
current practice, at the same time one specific example of a
transmission system will be numerically deduced to aid the
student in the use of the general equations.

This practical example will be a large power transmission
scheme for which the proper system, voltage, frequency, send-
ing and receiving apparatus, etc., must be determined; also the
best method of installation, protection, etc., and, finally, some
interesting features in the design of the apparatus involved.

That particular problem is to transmit 20,000 kw. 150 miles,
for railway and other power purposes; and, independently
thereof, 30,000 kw., 100 miles, for lighting.

The first section of the book deals with the transmission line
proper, the choice of system, voltage, distance between trans-
mission wires, number of lines in multiple, line constants,
frequency, transformer connections and telephone circuit and
cost of the line. The second with the power station proper,



some problems in thermo-dynamics, electrical generators,
methods of control,' and switchboard arrangements. The
problems in thermo-dynamics are included although they do
not properly belong in a treatise on electrical engineering,
since the subject is daily becoming more important and the
literature on the effect of superheat , vacuum, etc., is scant and
not readily available at the present time. The third with the
arrangement of the receiving stations, their apparatus, control,
method of secondary distribution, etc.

Sections I and II are incorporated in the first volume; section
III, in the second.


UNDER this heading is included the discussion of the
following :

First. System. This is determined by commercial condi-
tions largely the cost of the conductor in the transmission

Second. The Voltage. The upper limit is given by experi-
ence. At present a line potential of 60,000 volts is successfully
used, and 100,000 volts is seriously considered. Such high
voltages are not resorted to unless necessary on account of
commercial conditions.

Third. Distance between Transmission Wires. This is gov-
erned by practical experience.

For voltages from 2300 to 6600 the distance is 2 ft. 4 in.
, For voltages from 10,000 to 20,000 the distance is 3 ft. 4 in.

For voltages from 20,000 to 30,000 the distance is 4 ft.

For voltages from 30,000 to 50,000 the distance is 5 ft.

For voltages from 50,000 to 60,000 the distance is 6 ft.

Fourth. Line Constants. Resistance, induction coefficient
and capacity are obtained by calculations.

Fifth. Frequency. Partly governed by commercial consid-
erations but also by " the natural period," which is depending
upon the " line constants."

Sixth. Transformer Connections. Under this heading also
comes the decision of using a grounded or an ungrounded sys-
tem. This is largely governed by theoretical considerations, and
to some extent by the proximity of trunk lines, of telephone or
telegraph wires.

Seventh. Telephone Line. The arrangement and protection
are governed by theoretical considerations.



Since the cost of the transmission line is usually the largest
part of the investment, it is evident that of the alternating
current systems, only the three phase, which requires least
copper, can be considered. Until recently this system had no
rival, but with the introduction of some rather important direct
current installations in Europe, this latter, as well as the three
phase, needs discussion.

Comparing the various systems on the basis of same maxi-
mum value of potential between conductors, we find the follow-
ing relation between the amount of copper required :

Single phase system 100

Two phase four wire . 100

Two phase three wire . . 146

Three phase three wire 75

Direct current 50

It is evident from this that, if there is any choice at all, it
lies between the direct current and the three phase systems;
indeed, were there no other considerations, the direct current
system would be chosen, since it requires but two thirds of the
copper of the three phase system, and even this amount could be
cut in half by using ground as return and only one conductor.

These, indeed, are the arguments which have made the
direct current high potential systems possible.

However, the drawbacks are:

First. The enormous complication of the generating and
receiving stations, which must involve a large number of units
connected in series; since, at the best, each unit can be made
for only about 6000 volts.

Second. The difficulties, not to say the impossibility, of
future increase of such stations, which are obviously a conse-
quence of the series connection of the generators and motors
and the limit imposed by the line potential.

Third. The ground return is not practical on account of
telephone and telegraph disturbances, and, to a large degree,
on account of the variation in potential around the grounded
terminal, which might be sufficient to cause serious accidents.


Fourth. It is not certain that the limit of potential is depend-
ing upon the maximum value. Electrolytic action seems to be
detrimental to the insulators; so that, though the available
practical data is scant, it looks as if the " effective " value of
the alternating current voltage gives about as much stress
on insulators as the same direct current voltage, though the
direct current voltage corresponds to the maximum value of
the alternating current wave.

Assuming that the effective alternating current potential is
comparable with the direct current voltage, the three phase
system would require but 75 per cent of the copper of the direct
current system.

Perhaps the relation between the equivalent voltage lies
between the two limits discussed above. If so, it would seem
as if the amount of copper necessary would be the same.

Considering, therefore, the problematic saving in copper and
the serious disadvantages of the direct current system and
the flexibility of the alternating current systems, there seems
to be, with the present knowledge of the high tension direct
current systems, no choice between the two.

The three phase system will, therefore, be more particularly
considered and used in the numerical examples referred to


Since the amount of line conductor is inversely proportional
to the square of the voltage, it is well to consider as high a
potential as is consistent with good engineering; provided, of
course, that the additional cost of insulators, transformers, etc.,
does not overbalance the saving in cost of the line conductor.

Numerous diagrams and more or less complicated equations
have been published which show, for a given cost of installation,
conductor, price of delivered energy, load factor, etc., just what
is the most economical line voltage.

These equations, however, are so complicated that very
little time would be gained (after deducing that necessary to
get confidence in the equation) over that required when several
different line voltages are investigated.

There seems to be an increasing tendency to go to higher
line voltage, partly because of experience gained, and partly


because the price of copper and aluminium has steadily

Sometimes the line voltage is determined by the generator
voltage. At present large slow-speed engine-driven generators
have been wound for about 20,000 volts, and it is possible that
this voltage is practicable also with turbo generators.

To do away with the step-up transformer, it will frequently
pay to adopt such line voltage as will permit connecting the
generators directly to the lines, although, considering the line
conductor alone, a higher voltage would be advisable.

At least one transmission system is to-day in operation,
which delivers power at 60,000 volts. Almost a dozen are
being built, so that ample experience with this voltage will
soon be available.

In the numerical example, this voltage will, therefore, be

Consider first the longest distance 150 miles. The power,
in that case, shall be used for railway load, involving the use of
rotary converters and direct current railway motors or trans-
formers and alternating current motors.

In the former case an excessive line loss is not practicable, on
account of the probability of " hunting," which phenomenon will
be discussed later in connection with this type of apparatus; in
the latter case it is not permissible, on account of the effects on
the speed and the lighting of the cars.

More than 15 per cent energy loss with full non-inductive
load ought therefore not to be permitted.

Depending upon the price commanded by the delivered energy
it may well be possible that a lesser line loss than 15 per cent
is permissible.

It is desirable to calculate the transmission system on the
basis of at least two different losses, and then from the estimated
total cost of installation judge which is preferable.

These cost estimates will be discussed in the latter part of
the section.

Although the load is almost always inductive, the line loss is
estimated on non-inductive operation, so that in reality the drop
in voltage is often considerably more than the assumed 7 oss.
This feature will be discussed in connection with the line calcu-




Let P be the full non-inductive input in kilowatts to the

receiving end of the line.
p be the percentage loss of delivered power due to full

load non-inductive current over the line resistance

(p expressed as an integer number, not a fraction;

thus, for instance, 15 for 15 per cent loss).
7 the full load non-inductive current in each phase.
r the resistance of each line, counting the distance as

that from generating station to end of line.
m the number of lines in the system.
We have then,

^- X P X 1000 = m X Pr,

p X P X 1000

or r =

100 X P X m

In a single phase system m = 2.
In a two phase system m = 4.
In a three phase system m = 3.
For the same maximum voltage between lines E, we have

T-, P X 1000

.bor a single phase system / =

For a two phase system 7 =
For a three phase system 7 =


P X 1000

P X 1000


Therefore, the resistance of each conductor can also be
written as

.000005 j)W f
r - -^p , for single phase,

.00001 p E 2
r - , for two phase,

.00001 p E 2
and r = - ~ , for three phase.


From the above it is evident that the amount of copper in
the single phase and two phase systems is the same. Further-
more, since the resistance of each of the two phase lines is the
same as that of the three phase lines, and the three phase system
uses three lines only, it follows that the three phase system uses
only 75 per cent as much conductor as the two phase system.

Returning now to the numerical example and substituting
in the above equation for the three phase system, we get

.00001 X' 15 X 60,000 2
' 20,000 =27 ohms. , ; .

The resistance of each phase is therefore


= 0.18 ohm per mile.

Referring to the wire table given in the last paragraph of
this section, we find that two No. 000 B. & S. copper wires in
parallel will have practically this resistance.

Although formulae are very convenient, it is very desirable
to know how to do without them; we will, therefore, arrive at
the proper line conductor in another way.

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Online LibraryErnst Julius BergElectrical energy, its generation, transmission, and utilization → online text (page 1 of 13)